The overall goal of this project is to develop statistically proper and efficient methods for analyzing the gap times between recurrent infections after hematopoietic cell transplantation (HCT). Infection is one of the most common problems after HCT and accounts for substantial morbidity and mortality. Many patients experience infectious complications repeatedly over time. To characterize the natural history of infectious complications after transplantation and to identify risk factors related to infections, ne needs innovative multivariate statistical methods which can efficiently use the time information of recurrent infectious events and the rich data of patient and transplant related characteristics routinely collected by transplant centers. Existing statistical methods for recurrent gap time data typically assume that patients are enrolled due to the occurrence of an event of the same type as the recurrent event or assume that all gap times, including the first gap, are identically distributed. Applying these methods on the post-transplant infection data, thus ignore event types, will inevitably lead to incorrect inferential results because the time from the transplant t the first infection has a different biological meaning than the gap times between recurrent infections after the first infection. Alternatively, one may only analyze data after the first infetion to make the existing recurrent gap time methods applicable, but this introduces selection bias because only patients who have experienced infections are included in the analysis. Other naive methods may include using the univariate survival analysis methods, e.g., the Kaplan-Meier method and the Cox regression model, on the first infection only data or using the bivariate survival data methods, e.g., the Huang-Louis estimator and the Lin-Sun-Ying estimator, on the data up to the second infections. Hence, all subsequent infection data beyond the first or the second infectious events will not be utilized in the analysis, which will lead to inefficient estimation or a decreased power. In this application, we propose to develop efficient statistical methods for analyzing the gap times between recurrent infections after transplant. In Specific Aim 1, we will develop the nonparametric estimation method for the joint distribution of the time from the transplant to the first infection and the gap times between recurrent infections for the population of interest. In Specific Aim 2, we will develop regression model, which can incorporate patient and treatment characteristics to study the risk factors of infectious complications of the transplant patients. All proposed methods will be evaluated using extensive simulation studies and the analysis of an existing data set collected from patients who received their first HCT from the University of Minnesota between January 1, 2000 and December 31, 2010. User-friendly programs written in R language will be developed for the proposed methods and made freely available for public use. The proposed research holds both methodological significance and scientific significance. First, the methodology will be generally applicable to other recurrent gap time data with the initial event being different from all the subsequent events, which design is frequently encountered in longitudinal studies. Second, the proposed research holds the potential to advance the understanding of the natural history of infectious complications after hematopoietic cell transplantation and to help identify risk factors and improve the post- transplant care of patients.